Question 182875
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If <i>q</i> and <i>r</i> are complementary and If <i>q</i> and <i>s</i> are supplementary, then the following relationships hold:


*[tex \LARGE \text{          }\math q + r = 90]



*[tex \LARGE \text{          }\math q + s = 180]


If we subtract 90 from both sides of the second equation:


*[tex \LARGE \text{          }\math q + s - 90 = 90]


But since we have the first relationship, we can substitute:


*[tex \LARGE \text{          }\math q + s - (q + r) = 90]


A little distributive property and collection of like terms:


*[tex \LARGE \text{          }\math q + s - q - r = 90]


*[tex \LARGE \text{          }\math s - r = 90]


Yielding the desired relationship.

John
*[tex \LARGE e^{i\pi} + 1 = 0]
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